We present a study of the infrared properties of X-ray selected , moderate luminosity ( i.e , L _ { X } = 10 ^ { 42 } -10 ^ { 44 } { ergs~ { } s ^ { -1 } } ) active galactic nuclei ( AGNs ) up to z \approx 3 , in order to explore the links between star formation in galaxies and accretion onto their central black holes . We use 100 { \umu m } and 160 { \umu m } fluxes from GOODS- Herschel – the deepest survey yet undertaken by the Herschel telescope – and show that in the vast majority of cases ( i.e. , > 94 per cent ) these fluxes are dominated by emission from the host galaxy . As such , these far-infrared bands provide an uncontaminated view of star formation in the AGN host galaxies . We find no evidence of any correlation between the X-ray and infrared luminosities of moderate AGNs at any redshift , suggesting that star-formation is decoupled from nuclear ( i.e. , AGN ) activity in these galaxies . On the other hand , we confirm that the star formation rates of AGN hosts increase strongly with redshift ; by a factor of 43 ^ { +27 } _ { -18 } from z < 0.1 to z = 2 - 3 for AGNs with the same range of X-ray luminosities . This increase is entirely consistent with the factor of 25–50 increase in the specific star formation rates ( SSFRs ) of normal , star-forming ( i.e. , main-sequence ) galaxies over the same redshift range . Indeed , the average SSFRs of AGN hosts are only marginally ( i.e. , \approx 20 per cent ) lower than those of main-sequence galaxies at all surveyed redshifts , with this small deficit being due to a fraction of AGNs residing in quiescent ( i.e. , low-SSFR ) galaxies . We estimate that 79 \pm 10 per cent of moderate luminosity AGNs are hosted in main-sequence galaxies , 15 \pm 7 per cent in quiescent galaxies and < 10 per cent in strongly starbursting galaxies . We derive the fractions of all main sequence galaxies at z < 2 that are experiencing a period of moderate nuclear activity , noting that it is strongly dependent on galaxy stellar mass ( M _ { stars } ) ; rising from just a few per cent at M _ { stars } \sim 10 ^ { 10 } M _ { \odot } to \gtrsim 20 per cent at M _ { stars } \geq 10 ^ { 11 } M _ { \odot } . Our results indicate that it is galaxy stellar mass that is most important in dictating whether a galaxy hosts a moderate luminosity AGN . We argue that the majority of moderate nuclear activity is fuelled by internal mechanisms rather than violent mergers , which suggests that high redshift disk instabilities could be an important AGN feeding mechanism .